The so-called “bullet effect” refers to the perforation of a rockfall protection mesh by impact of a small block, which has a kinetic energy lower than the design value, where the design value is determined through tests with relatively large blocks. Despite playing a key role in the overall performance of a flexible rockfall barrier, this phenomenon is still poorly understood at present. An innovative approach for quantitatively characterizing this effect based on dimensional analysis is proposed in this paper. The analysis rests on a hypothesis that the relevant variables in the impact problem can be combined into three strongly correlated dimensionless parameters. The relationship between these dimensionless parameters (i.e., the scaling relationship) is subsequently investigated and validated by means of data generated with a finite element model. The validation process shows that the dimensionless parameters are apt and that the proposed scaling relationship characterizes the bullet effect with a reasonable level of accuracy. An example from the literature involving numerical simulation of a full rock barrier is considered, and satisfactory agreement between the calculated performance of the barrier and that predicted by the established scaling relationship is observed.
This is a preview of subscription content, access via your institution.
Buy single article
Instant access to the full article PDF.
Tax calculation will be finalised during checkout.
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
Tax calculation will be finalised during checkout.
Anderheggen E, Volkwein A, Grassl H (2002) Numerical simulation of highly flexible rockfall protection systems. In: Proceedings of Fifth World Congress on Computational Mechanics. Vienna, Austria
Arndt B, Ortiz T, Turner AK (2009) Colorado’s full-scale field testing of rockfall attenuator systems. Transp Res E-Circular, E-C141. Transportation Research Board, Colorado
Bertolo P, Oggeri C, Peila D (2009) Full-scale testing of draped nets for rock fall protection. Can Geotech J 46(3):306–317. doi:10.1139/T08-126
Buckingham E (1914) On physically similar systems: illustrations of the use of dimensional analysis. Phys Rev 4:345–376
Buzzi O, Giacomini A, Spadari M, Fityus S (2011) Numerical modeling of a rock fall mesh perforation upon impact. In: Proceedings of the 13th International Conference of the IACMAG 2011. Sydney, Australia, pp 1141–1146
Cantarelli G, Giani GP, Gottardi G, Govoni L (2008) Modelling rockfall protection fences. In: The first world landslide forum—Proceedings. ICL, Tokyo, pp 103–108
Cazzani A, Mongiovì L, Frenez T (2002) Dynamic finite element analysis of interceptive devices for falling rocks. Int J Rock Mech Min Sci 39(3):303–321. doi:10.1016/s1365-1609(02)00037-0
De Col R, Cocco (1996) Motivazioni tecniche ed economiche per la standardizzazione di prove sulle opere paramassi nella Provincia Autonoma di Trento. In: Giornata di studio su “La protezione contro la caduta di massi dai versanti rocciosi”. GEAM, Torino, pp 65–72
Descoeudres F, Montani Stoffel S, Böll A, Gerber W, Labiouse V (1999) Rockfalls. In: Coping study on disaster resilient infrastructure. IDNDR, Zurich, pp 37–47
Duffy JD, Smith DD (1990) Field tests and evaluation of rockfall restraining nets. No. CA/TL-90/05, Final Report. California Dept. of Transportation, San Luis Obispo
EOTA (2008) Guideline for European technical approval of falling rock protection kits (ETAG 027). Brussels
Gerber W (2001) Guideline for the approval of rockfall protection kits. Swiss Agency for the Environment, Forests and Landscape (SAEFL), Swiss Federal Research Institute, Berne
Giani GP (1992) Rock slope stability analysis. Balkema, Rotterdam
Grassl H, Volkwein A, Anderheggen E, Ammann WJ (2002) Steel-net rockfall protection—experimental and numerical simulation. In: Seventh International Conference on Structures Under Shock and Impact. Montreal, Canada, pp 143–153
Hearn G, Barrett RK, Henson HH (1995) Testing and modeling of two rockfall barriers. In: Transportation research record, vol. 1504. National Research Council, Washington, pp 1–11
Johnson W (1972) Impact strength of materials. Edward Arnold, London
Langhaar HL (1951) Dimensional analysis and theory of models. Wiley, New York
Li QM, Jones N (2000) On dimensionless numbers for dynamic plastic response of structural members. Arch Appl Mech 70(4):245–254
Peila D, Oggeri C (2005) Barriere paramassi a rete - Tecnologia e criteri pregettuali. GEAM, Torino
Peila D, Pelizza S, Sassudelli F (1998) Evaluation of behaviour of rockfall restraining nets by full scale tests. Rock Mech Rock Eng 31(1):1–24
Volkwein A (2005) Numerical Simulation of flexible rockfall protection systems. In: Proceedings of Computing in Civil Engineering. ASCE, Cancun
Volkwein A, Melis L, Haller B, Pfeifer R (2005) Protection from landslides and high speed rockfall events—reconstruction of Chapman’s Peak Drive. In: IABSE Symposium Lisbon 2005. Structures and extrem events. IABSE Reports vol. 90, incl. CD: 8 p
About this article
Cite this article
Spadari, M., Giacomini, A., Buzzi, O. et al. Prediction of the Bullet Effect for Rockfall Barriers: a Scaling Approach. Rock Mech Rock Eng 45, 131–144 (2012). https://doi.org/10.1007/s00603-011-0203-0
- Rockfall barrier
- Kinetic energy
- Bullet effect
- Stress concentration
- Dimensional analysis